calculus

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how do I graph this using the first and second derivative and three sign charts.

i have to label the inflection point, extreme values and the intercepts also.

f(x)= x^3-6x^2

  • calculus -

    slope = 3 x^2 -12 x =3 x (x-4)

    second derivative (curvature)
    = 6 x - 12

    so the slope is 0 at x = 0 and at x = 4

    at x = 0
    is that a min or a max or in inflection point?
    second derivative = -12
    That is a maximum, starts down from there

    at x = 4 is that a min or a max or an inflection point?
    second derivative = +12
    so that is a minimum, starts up fro there.

  • calculus -

    Oh, intercepts
    y = x^3-6x^2
    0 = x^2 (x-6)
    bounced off x axis at x = 0
    crossed x axis at x = 6

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